Latterdenotes the second of the two objects mentioned, while the first one is referred to asthe former:
I met Max and Henry in the street. The former said "Hallo", but the latter didn't recognize me.
Lastis used with reference to time:
Lastyear we went to the Crimea.
The last denotes order and means not followed by anything else, while latest means most recent.
Byron’s last poem.
Akunin’s latest novel.
I usually watch the latestnews.
Read the last sentence, please.
Compare last year and the last year:
The last year’s exams are called “finals”.
We were discussing last year’s entrance exams.
Near - nearer nearest(denotes distance)
next(denotes time)
the next(denotes order)
Let's sit nearerto the stage.
We can have a snack in the nearestcafe.
What are your nearestplans?
I'll see Ann nextweek.
The nextstop is yours.
Note.Nextdenoting time takes no article with reference to the future and usually the definite article (sometimes no article) with reference to the past.